SOLVING NONLINEAR TWO-DIMENSIONAL VOLTERRA INTEGRAL EQUATIONS OF THE FIRST-KIND USING BIVARIATE SHIFTED LEGENDRE FUNCTIONS

Subject Areas : International Journal of Mathematical Modelling & Computations

Somayeh Nemati ¹ , Y. Ordokhani ²

1 - Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
2 -

Received: 2016-04-15 Accepted : 2016-04-15 Published : 2015-03-21

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Abstract :

In this paper, a method for finding an approximate solution of a class of two-dimensional nonlinear Volterra integral equations of the first-kind is proposed. This problem is transformedto a nonlinear two-dimensional Volterra integral equation of the second-kind. The properties ofthe bivariate shifted Legendre functions are presented. The operational matrices of integrationtogether with the product operational matrix are utilized to reduce the solution of the second-kind equation to the solution of a system of linear algebraic equations. Finally, a system of nonlinear algebraic equations is obtained to give an approximate solution of the main problem.Also, numerical examples are included to demonstrate the validity and applicability of themethod.